Question

In 2004, a magazine's circulation was about 1,000,000 readers. In 2014, the magazine had about 2,000,000 readers. Write a linear model that shows the number of readers, r, of the magazine t years after 2000.
r(t)=

Answer 1

Answer:

$r(t)=100,000t+600,000$

Step-by-step explanation:

Let

r ----> the number of readers (y-coordinate or dependent variable)

t ----> the number of years after 2000 (x-coordinate or independent variable)

Remember

2004 ----> represent t=4 years

2014 ----> represent t=14 years

we have the ordered pairs

(4,1,000,000) and (14,2,000,000)

step 1

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{2,000,000-1,000,000}{14-4}$

$m=\frac{1,000,000}{10}$

$m=100,000\frac{readers}{year}$

step 2

Find the equation of the line in point slope form

$r-r1=m(t-t1)$

we have

$m=100,000\\point\ (4,1,000,000)$

substitute

$r-1,000,000=100,000(t-4)$

step 3

Convert to slope intercept form

$r=mt+b$

isolate the variable r

$r-1,000,000=100,000t-400,000\\r=100,000t-400,000+1,000,000\\r=100,000t+600,000$

step 4

Convert to function notation

$r(t)=100,000t+600,000$